(b) The wave function for a quantum particle is given by Ψ(x) = Ax between x = 0 and x = 1.00, and Ψ(x) = 0 elsewhere. Find (i) the value of the normalization constant A, (ii) the probability that the particle will be found between x = 0.300 and x = 0.400, and (iii) the expectation value of the particle’s position

The frequency of vibrations of a vibrating violin string is given by f = 1 2l t ρ where l is the length of the string, t is its tension, and ρ is its linear density.† (a) find the rate of change of the frequency with respect to the following. (i) the length (when t and ρ are constant) (ii) the tension (when l and ρ are constant) (iii) the linear density (when l and t are constant) (b) the pitch of a note (how high or low the note sounds) is determined by the frequency f. (the higher the frequency, the higher the pitch.) use the signs of the derivatives in part (a) to determine what happens to the pitch of a note for the following. (i) when the effective length of a string is decreased by placing a finger on the string so a shorter portion of the string vibrates df dl 0 and l is ⇒ f is ⇒ (ii) when the tension is increased by turning a tuning peg df dt 0 and t is ⇒ f is ⇒ (iii) when the linear density is increased by switching to another string df dρ 0 and ρ is ⇒ f is ⇒

The dot diagram represents the motion of the motorcycle as it moves from left to right

Which composition of water moves to begin a deepwater current?